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Would you decrease your impact impulse by jumping during the fall? Yes When? Soon enough that it's before impact, late enough that you don't hit the ceiling of the elavator. Beyond that I don't think it matters much. Would it help if you jump inside a free falling elevator? Probably not. Indeed I expect it would make things worse. The ...

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The solution is actually strange for me. It assumes that the distance traveled by each car (in the CM frame) during the acceleration (crumpling) is also equal to the crumple length of each car, but is not always the case. Following the assumption of the solution: In the CM frame, the heavier car moves slower than the lighter car. So that at the moment that ...

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Your explanation is almost exactly the same as the one which you say that you do not understand. So what exactly is confusing you? If $v_p-v_q$ is due south it does not necessarily follow that $r_p-r_q$ is also due south. For example, Q could be stationary while P moves due south, but the initial position of P could still be east or west or even south of Q ...

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Relative to Q, Q is not moving, and P is north of Q. $\vec v_p - \vec v_q$ is the velocity of P relative to Q. So basing on that, and knowing that P is exactly north of Q initially, we only need to know if P is going south relative to Q. Also, this means that $r_p-r_q$, the position of P relative to Q, is due north. Then, we should expect the velocity of P ...

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This is a tricky question. I think you are all right and this problem, because using momentum, is valid for both elastic and inelastic problem. the tricky part is, particle A cannot penetrate particle B. If, they collide, particle A moves at -97.5m/s and particle B moves with -2m/s, do you think that is possible? So if particle A initial velocity is ...

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